Turn on a multi-functional pressure cooker (such as Instant Pot(R)) and select Saute function.
Melt butter and cook onion until soft and tender, about 3 minutes.
Add chicken; cook until golden and crispy, about 5 minutes.
Place diced tomatoes, kale, chicken broth, salt, garlic powder, oregano, and black pepper in the pot.
Close and lock the lid.
Select high pressure according to manufacturer's instructions; set timer for 10 minutes.
Allow 10 to 15 minutes for pressure to build.
Release pressure using the natural-release method according to manufacturer's instructions, about 10 minutes.
Complete releasing pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes.
Unlock and remove the lid.